Holocene melting of the West Antarctic Ice Sheet driven by tropical Pacific warming

The primary Antarctic contribution to modern sea-level rise is glacial discharge from the Amundsen Sea sector of the West Antarctic Ice Sheet. The main processes responsible for ice mass loss include: (1) ocean-driven melting of ice shelves by upwelling of warm water onto the continental shelf; and (2) atmospheric-driven surface melting of glaciers along the Antarctic coast. Understanding the relative influence of these processes on glacial stability is imperative to predicting sea-level rise. Employing a beryllium isotope-based reconstruction of ice-shelf history, we demonstrate that glaciers flowing into the Amundsen Sea Embayment underwent melting and retreat between 9 and 6 thousand years ago. Despite warm ocean water influence, this melting event was mainly forced by atmospheric circulation changes over continental West Antarctica, linked via a Rossby wave train to tropical Pacific Ocean warming. This millennial-scale glacial history may be used to validate contemporary ice-sheet models and improve sea-level projections.

I ncreasing ice loss and sea-level contribution from Antarctica since the early twenty-first century is caused by rapid thinning, retreat, and acceleration of major outlet glaciers of the West Antarctic Ice Sheet (WAIS) 1 . Recent WAIS mass loss has been focused within the Amundsen Sea Embayment (ASE), which may indicate the beginning of marine ice sheet instability 2,3 . Ice mass loss since the 1990s is attributed to the ocean-driven melting of ice shelves by the upwelling of relatively warm Circumpolar Deep Water (CDW) onto the West Antarctic continental shelf 1,4 . Precipitation and warming over West Antarctica was also more elevated in the 1990s than at any time over the last 200 years, linked to higher tropical Pacific Ocean temperatures 5,6 . Atmospheric rivers (narrow bands with enhanced water vapour flux) associated with this tropical-polar teleconnection represent 100% of summer surface melt in Marie Byrd Land 7 , presenting an additional contribution to global sea-level rise from the atmospheric-driven melting of glaciers along the West Antarctic coast. Significant uncertainty therefore remains for the permanence of increasing ice loss, projected contributions to sea level, and the dominant driving mechanisms behind mass balance change 1 . Integrated models predicting the timing and rate of future Antarctic ice mass loss rely on validation from long-term (10 2 -10 3 yr) records of past ice-sheet change 8,9 , and therefore require glacial reconstructions since the Last Glacial Maximum (LGM) 10 .
Marine records from the ASE reveal that the Amundsen sector of the WAIS (Fig. 1a) reached its modern limits by the Early Holocene 11 (Fig. 1b), driven by upwelling CDW onto the continental shelf due to a southerly position of the Southern Hemisphere westerly wind belt 12 . However, the mechanism behind subsequent early-to-mid-Holocene thinning of ice streams surrounding the ASE 13,14 is still not well understood 15 . Here we apply beryllium (Be) isotopes, a proxy for glacial processes, to provide a 10.3 kyr history of the Cosgrove Ice Shelf (CIS) in the eastern ASE (Fig. 1b). We measured the reactive 10 Be abundance ([ 10 Be] reactive ), 9 Be abundance ([ 9 Be] reactive ) and 10 Be/ 9 Be ratios in marine sediments collected during the IB Oden Southern Ocean cruise (OSO-0910) 16 ("Methods"). Kasten cores KC-15, KC-16 and KC-17 were collected just offshore the modern terminus of the CIS in Ferrero Bay (Fig. 1c). Beryllium isotope records are supported by published multi-proxy analysis of total organic carbon (TOC), total nitrogen (TN), microfossil abundance and assemblages (diatoms and foraminifera), and magnetic susceptibility (MS), which together provide a record of Holocene productivity and grounding line retreat 17 . Beryllium isotope records from KC-15 are compiled onto a new age-depth model (Fig. S1) to elucidate the timing of CIS retreat during the Holocene.
The strong correlation between [ 10 Be] reactive and 10 Be/ 9 Be ratios in all three cores (Tables S3-S5) suggests the rise in [ 10 Be] reactive is largely controlling variation in the 10 Be/ 9 Be ratios. Reactive 10 Be, and therefore 10 Be/ 9 Be, displays a similar trend to TOC and TN in KC-15, KC-16, and KC-17 (Tables S3-S5). Magnetic susceptibility records a negative correlation to Be isotopes (Tables S3-S5), representing a lithologic transition from coarse-grained sediments with high sand content (% sand =  64,65 , satellite imagery 66 , radiocarbon dates and terrestrial cosmogenic nuclide dates 11,13,14,48 for the Amundsen Sea Embayment, Pine Island Trough (PIT), and Pine Island Bay (PIB). c Location of OSO-0910 KC-15, KC-16, and KC-17 in Ferrero Bay with multibeam swath bathymetry 16 . Maps were constructed using Quantarctica from the Norwegian Polar Institute 67 .
14-46%) at the base of the core to overlying fine-grained sediments that are rich in silt and clay 17 . Diatom abundance correlates with Be isotopes in KC-15 and KC-17, with the exception of [ 9 Be] reactive in KC-17, however, diatoms were not counted at the same sampling interval making a direct comparison with Be concentration difficult (Tables S3, S5).
The sediments from KC-15 record the last~10.3 kyr of glacial history for Ferrero Bay and the CIS. According to our new age model ( Fig. S1; Table S1), Be isotope data reveal three periods of interest ( Fig. 3a): (1) in the Early Holocene, between~10.3 and 9.8 kyr BP, the 10 Be/ 9 Be ratios are low at~0.42; (2) transitioning from the Early Holocene to Mid-Holocene, 10 Be/ 9 Be increases between~9.8 kyr BP and~5.9 kyr BP from~0.46 to~2.33; (3) then through the Late Holocene, 10 Be/ 9 Be ratios are relatively constant at~2.3. During the Late Holocene, 10 Be, 9 Be, TOC, and TN potentially display millennial-scale variability, increasing after 1.4 kyr BP (Fig. 2), but higher temporal resolution would be needed to support this notion. In the following section, we discuss the environmental and physical factors that could contribute to Be isotope variation in Ferrero Bay during the Holocene.
Beryllium isotope systematics in glacial environments. The cosmogenic isotope 10 Be is produced by the interaction of cosmic rays with oxygen and nitrogen in the atmosphere and is deposited to the Earth's surface via dust or precipitation 18 , becoming enriched in surface waters under high precipitation such as the equatorial Pacific (~1100 atoms/g) 19,20 . Beryllium-9, on the other hand, is released during the chemical weathering of silicate minerals 18 and is enriched in waters near high fluvial or aeolian inputs e.g., equatorial Atlantic surface waters in proximity to Saharan dust plumes 20 . Away from regions of high surface inputs, such as the South Pacific, Be follows a general profile of nutrient scavenging with a depletion in the surface mixed layer (~750 atoms/g) and an enrichment in deeper waters (~2000 atoms/g), reflecting the high scavenging potential of Be [19][20][21] . The 10 Be/ 9 Be of Pacific seawater has an average ratio of~1 × 10 −7 but ranges from~0.4 × 10 −7 to~3.1 × 10 −7 in equatorial surface waters of the Atlantic and Pacific due to additional inputs of 9 Be and 10 Be, respectively 20 . The disparate sources of 10 Be and 9 Be led to fluctuations in the 10 Be/ 9 Be of seawater, recorded in marine sediments and ferromanganese crusts, over Quaternary climate cycles, due to large regional variability in fluvial inputs between glacial and interglacial periods 22 .
The Be isotope composition of marine sediments on the continental shelf is controlled by the relative mixing of two reactive phases, one sourced from the coast, defined by low 10 Be/ 9 Be reactive due to the input of fluvial 9 Be, and another sourced from entraining seawater, defined by high 10 Be concentrations and 10 Be/ 9 Be ratios 23 . The high 10 Be/ 9 Be of seawater is augmented in polar regions by the input of 10 Be from atmospheric sources 18,24 and/or the melting of sea ice ([ 10 Be] =~0.25-0.65 ×10 4 atoms/g) 25 and ice sheets ([ 10 Be] = 1-3 × 10 5 atoms/g) 26 , which act to accumulate meteoric 10 Be overs years to millennia, leading to exceptionally high surface water ratios which have been observed in the Deep Canadian Basin (~1.4 × 10 −7 ) 25 and Drake Passage (~3.3 × 10 −7 ) 19,20 , respectively. The export of meltwater signals further offshore may be enhanced by the calving of icebergs and their subsequent passage off the continental shelf 27 .
The separate transport pathways and sources of 10 Be and 9 Be in ice sheets has allowed Be in glaciomarine sediments to become a powerful proxy of glacial dynamics 24,27-31 . Open marine sediments close to the calving line of ice shelves are defined by higher Be concentrations and 10 Be/ 9 Be ratios relative to other glacial environments due to efficient scavenging of Be by diatoms from seawater defined by higher overall ratios as previously discussed 24,28 . Lower 10 Be concentrations and 10 Be/ 9 Be ratios can be found in sub-ice shelf sediments, induced by lower productivity and limited advection of open marine material into the ice-shelf cavity 24,27,28 . Finally, sediments in proximity to the grounding line receive 9 Be from the basal zone during glacial erosion leading to exceptionally low 10 Be/ 9 Be ratios 27,31 . Here, we relate Be isotope variation in Ferrero Bay to three main processes: (1) environmental setting; (2) depositional processes; and (3) meltwater contribution (Fig. 4).
The Cosgrove Ice Shelf in the Holocene. Bathymetric surveys reveal that grounded ice occupied Ferrero Bay during the LGM as part of the larger ice stream in the Cosgrove-Abbot Trough, which reached the continental shelf edge north of the Abbot Ice Shelf 11,32,33 (Fig. 1b) Calendar Age (kyr BP) 10 Be/ 9 Be (10 ) -8 a Fig. 3 Ice-shelf history of the CIS for the Holocene. The 10 Be/ 9 Be ratios (a) and relative 10 Be vs. 9 Be relationship (b) in OSO-0910 Kasten core KC-15. Error bars represent 2σ confidence intervals (Fig. S1) Open marine Sub-ice-shelf Subglacial

Ice flow
Be Be Open marine Sub-ice-shelf Subglacial b Melting of icebergs and sea ice near the calving line releases 10 Be which is rapidly scavenged by diatom frustules and organic matter before becoming advected under the ice-shelf with other marine material by ocean currents such as intruding CDW. c Meltwater rich in 10 Be is released from the ice-shelf base and scavenged by fine-grained sediment delivered from the grounding line. This figure was modified from Yokoyama et al. 24 and White et al. 27 . and the development of a more distal environmental setting (Figs. 2a, c, 3a and 4a (Figs. 2 and 4a). The relative change in Be concentration across these various glacial environments is likely to be controlled by depositional processes such as dilution, scavenging efficiency, and/or extraction efficiency 22 , much like the percentage of TOC 35 . From the bottom of the cores to~111 cmbsf in KC-15 and KC-17, TOC is likely diluted by the input of coarse-grained clastic material from the grounding line with a high sand content of 27-46% (ref. 17 ). From~111 cmbsf, TOC is largely controlled by steadily increasing accumulation rates (calculated from the new agedepth model) of fine-grained (% sand ≦ 12.5%) sediment upsection, which allows for a more rapid passage of organic carbon through the near-surface zone, reducing its degradation 35 . Reactive 10 Be, and to a lesser extent 9 Be, displays a strong correlation to TOC ( Fig. 2; Tables S3-S5), suggesting Be concentration may also be largely controlled by dilution and/or scavenging efficiency. A similar lithological control is observed in Baffin Bay whereby [Be] reactive and 10 Be/ 9 Be are relatively low over the last glacial cycle due to the poor scavenging efficiency of coarse-grained carbonate-rich material but Be isotopes increase by over an order of magnitude during ice-surging events associated with the production of fine-grained feldspar-rich glacial flour 36 . The percentage of TOC and Be concentration in Ferrero Bay sediments may also be related to productivity (i.e., diatom and foraminifera abundance) in the overlying water column or the advection of biogenic material into the ice-shelf cavity. However, the diatoms were not counted at the same sampling interval and other organic plankton such as dinoflagellates are not included in previous studies 17 , limiting a direct comparison between TOC, Be abundance, and productivity.
Much like Be isotope concentration, the relationship between relative 10 Be and relative 9 Be is largely controlled by extraction efficiency, scavenging efficiency, and/or dilution, generally defined by a 1:1 relationship. Changes in the gradient of this relationship above or below one is driven by an additional input of 9 Be or 10 Be, respectively 22,37 . The relative 10 Be vs. relative 9 Be relationship of sediments from Baffin Bay and offshore Wilkes Land are defined by a gradient less than one (Fig. 3b) controlled by the additional flux of meltwater-derived 10 Be from nearby ice sheets 36,37 . This leads to higher 10 Be/ 9 Be ratios during periods of intense glacial discharge such as Heinrich events 36 and Pliocene interglacials 37 . Sediments from KC-15 to KC-17 display a similar relationship to Baffin Bay and offshore Wilkes Land (Fig. 3b) indicating an additional input of meltwater-derived 10 Be to Ferrero Bay may be contributing to the increase in 10 Be/ 9 Be ratios from~9.8 kyr BP to~5.9 kyr BP (Fig. 3a).
Meltwater input to Ferrero Bay is derived from one of two sources: (1) the calving of ice shelves and melting of icebergs, the meltwater of which is subsequently advected under the CIS (Fig. 4b), or (2) the basal and/or surface melting of the CIS (Fig. 4c). From 10.3 to 9.8 kyr BP, limited productivity of diatoms and calcareous foraminifera resulted from the advection of offshore currents under the Amundsen Sea ice shelf, as evidenced by low benthic productivity and the presence of the planktic foraminifer N. pachyderma, suggesting that ocean currents accessed the grounding line at this time 17,33 (Fig. 2a, c). During this period, [ 10 Be] reactive and 10 Be/ 9 Be are at their lowest, however-indicating a negligible amount of Be is advected from the calving line or from offshore currents (Fig. 4b).
From 9.8 to 2.3 kyr BP, diatom abundance is low, and calcareous foraminifera and benthic productivity are low but present, indicative of a distal glacio-marine environment and limited advection under the extended paleo-ice shelf 17,33 (Fig. 2a, c). During the period, [ 10 Be] reactive and 10 Be/ 9 Be increase (Fig. 2a, c), indicating that the majority of Be is not sourced by water flowing from the continental shelf and is more likely associated with subglacial water flowing out from beneath the ice sheet (Fig. 4c). This is supported by observations from Lake Maruwan Oike, East Antarctica, which records peak [ 10 Be] reactive and 10 Be/ 9 Be during a brackish transition to lacustrine conditions, implying Be is derived from the melting of local glaciers 29 . Importantly, a benthic foraminifera species thought to be associated with CDW, B. aculeata, is present at 51 and 71 cmbsf in KC-15 (Fig. 2a), indicating CDW incursion during the Mid-Holocene 17 , but the advection of this offshore water mass apparently had limited influence over Be isotope values which remain high but relatively constant during this time.
To summarise, Be isotope data from Ferrero Bay suggests the CIS underwent a dramatic shift from the Early-to-Mid-Holocene: (1) the grounding line was proximal to KC-15 prior to~9.8 kyr BP during the Early Holocene, with a permanent ice-shelf extending beyond KC-17 into the ASE; (2) the grounding line retreated from the Early-to-Mid-Holocene between~9.8 kyr BP and~5.9 kyr BP, associated with melting of the CIS and its paleoice stream; (3)  Atmospheric warming led to Holocene melting. Melting and retreat of the CIS and its paleo-ice stream recorded here corresponds well to a respective~560 m and~150 m thinning of the Pope Glacier 18 and Pine Island Glacier 16 from 9 to 6 cal kyr BP and 8 to 6 cal kyr BP, indicating a widespread melting event within the Amundsen Sea sector of the WAIS (Fig. 5a). Early Holocene deglaciation of PIB is linked to the enhanced upwelling of relatively warm CDW (Fig. 5c) into the ASE 12,33 (Fig. 5b). Benthic δ 13 C data from PIB records a rapid reduction of CDW inflow at 9 kyr BP while planktic δ 13 C data display a gradual decline between 10.4 and 8 kyr BP (Fig. 5b), associated with a lessening of CDW heat supply 12,38 (Fig. 5c). Sediments studied here likely correspond to "Unit 1" and "Facies 3" in cores from PIT 33 and PIB 32 , respectively, representing a switch from proximal glacimarine sediments accessed by warm water flowing onto the continental shelf before~9.6 kyr BP, as evidenced by the presence of N. pachyderma (Fig. 2a, c) 17 , to distal meltwaterderived glacimarine sediments, devoid of biogenic material, emanating from beneath the ice sheet by~7.8 ka BP 33 . The 10 Be/ 9 Be ratios from KC-15 are at their lowest during maximum CDW incursion into the PIB region, increasing after 9 kyr BP (Fig. 5a, b). This suggests that early-to-mid-Holocene retreat of the CIS was generally not associated with the upwelling of CDW into Ferrero Bay, albeit some contribution is constrained to the Mid-Holocene between~5.9 and~4 kyr BP as inferred by the presence of the CDW-associated benthic foraminifer B. aculeata 17 (Fig. 2a).
During the Holocene, the Southern Hemisphere westerly winds were at their weakest between 11 and 9 cal kyr BP, gradually intensifying during the Mid-Holocene to maximum values at5 cal kyr BP 39 , associated with a poleward migration of the westerly wind belt between 8.5 and 5.5 cal kyr BP 40 (Fig. 5d).
The southerly shift in the westerly winds coincides with a progressive warming of the tropical Pacific 41 (Fig. 5e) and greater thermal contrast across the zone of strong westerlies 42 . A steeper west to east upper-ocean temperature gradient and intensified Walker circulation in the equatorial Pacific led to a second peak in thermocline warming of the Indo-Pacific warm pool during the Mid-Holocene, reaching peak warming between 7 and 6 cal kyr BP 43 (Fig. 5e). Tropical Pacific warming can generate an atmospheric Rossby wave train that influences atmospheric circulation over the Amundsen Sea, leading to advection of warm air onto continental West Antarctica (i.e., Ellsworth Land and Marie Byrd Land), associated with cooling and greater sea-ice formation around the Antarctic Peninsula 5 , suggesting a link between Pacific warming and ice sheet thinning around the ASE 7,44 .
A southerly position of the westerly jet and an increase in atmospheric moisture content led to a poleward displacement and a higher frequency of Pacific atmospheric rivers during the Mid-Holocene 45 . A strengthening of the Amundsen Sea Low increased cyclonic-driven precipitation over continental West Antarctica between 9 and 6 kyr BP, as evidenced by a relatively small surface air temperature warming coupled to a dramatic increase in accumulation rates at the WAIS Divide ice core 46 (Fig. 5f). Intense rainfall would have enhanced surface melting over the West Antarctica coast, thus decreasing surface albedo and increasing regional melt, while higher mixed-phase cloud cover would have reduced radiative cooling and therefore meltwater refreezing 7,44 . Furthermore, if atmospheric rivers travel perpendicular to coastal mountain ranges near the Amundsen Sea, the resulting föhn winds can enhance surface melt through adiabatic warming of descending dry air 7 .
Surface melting and/or surface-meltwater-enhanced calving of floating ice shelves would trigger rapid ice flow accelerations in outlet glaciers 9 , leading to retreat of the CIS and meltwater discharge of 10 Be, via basal melting or meltwater injection from surface melt ponds and lakes through ice fractures and moulins 47 , and thinning of ice streams along the Ross and Amundsen Sea coasts 13,14,48,49 during the Early-to-Mid-Holocene (Figs. 4c and 5a). Conversely, an ice core from the east Antarctic Peninsula records a cooling trend from 10 to 8 cal kyr BP 50 , associated with a reduction in glacial discharge 51 and greater sea-ice formation 52 , while sediment core biomarkers suggest surface water cooling 38   13,14 . b δ 13 C values of benthic (grey diamonds) and planktic (black diamonds) foraminifera relative to estimated values for the CDW (yellow box) and AASW (blue box) from PS75/160 and PS75/167 (Fig. 1b) 12 . c Five-point moving average of sea surface temperature (SST) estimated for the Palmer Deep, western Antarctic Peninsula shelf (red line; ODP 1098, Fig. 1a) and Mg/Ca ratios of benthic foraminifera as a semiquantitative representation of bottom-water temperatures within PIB (black crosses; PS75/160, Fig. 1b) (Fig. 1a). The grey box highlights the interval of 9 to 6 cal kyr BP.
( Fig. 5c) along the west Antarctic Peninsula between 9 and 6 cal kyr BP. The cooling trend observed along the Antarctic Peninsula at the same time as a warming trend in the ASE is consistent with a teleconnection between tropical Pacific warming and atmospheric circulation over West Antarctica 5 . Hence, we suggest that higher tropical Pacific Ocean sea surface temperatures led to atmospheric warming and higher precipitation over continental West Antarctica, inducing melting and retreat of the CIS and thinning of other glaciers in the ASE between 9 and 6 cal kyr BP.
Outlook and future research. Presently, glaciers flowing into the ASE are the main Antarctic contribution to global sea-level rise, averaging 0.23 ± 0.02 mm yr −1 between 1992 and 2013 (ref. 2,3 ). The driving mechanism of sea-level rise acceleration has been attributed to ocean-driven melting of ice shelves that buttress glacial flow 1,4,12 . However, atmospheric rivers associated with tropical-polar teleconnections present a mechanism for substantial contribution to seasonal surface melt over continental West Antarctica as well 7 . Greater atmospheric moisture content and poleward expansion of the Hadley cells under rising greenhouse gas emissions suggest atmospheric river climatology is already beginning to resemble that of the Mid-Holocene 45 , possibly linked to extensive melt events along the Ross and Amundsen Sea coasts since the 1990s 6,7,44 . Our study suggests that future warming and increasing precipitation brought by enhanced atmospheric river activity could contribute to further surface melting and significant glacial discharge into the ASE. This information is vital for validating numerical models, thereby improving future predictions of sea-level rise 8,9,53,54 which is currently estimated to be as much as 1 m from Antarctica by the end of the twenty-first century 9 . Here, we demonstrate that Be isotopes can be successfully employed alongside other sediment and biological proxies to reconstruct past changes in depositional environment, ice shelf extent, and meltwater input-a parameter that is completely missing from most glacial records since the LGM 11,27 . However, uncertainty remains owing to the multiple sources and processes influencing the Be isotopes systematics of glacimarine sediments 27 . Future work will need to constrain the Be abundance in sea ice, ice sheets, and shelf waters, whilst also determining how Be is incorporated into sediments from the grounding line to the continental slope.

Methods
Study location and core sampling. Ferrero Bay is located within eastern PIB in the ASE (Fig. 1b), reaching a maximum depth of~1300 m to the north and an average of~700 m to the south near the Canisteo Peninsula (Fig. 1c) (Fig. 1c). All three cores generally consist of clays ranging from clayey sand to greenishblueish clay (Fig. 2) and record local glacial history, biological productivity, and oceanographic conditions during the Holocene 17 . KC-15 and KC-17 are divided into four units based on sedimentological, geochemical, and palaeontological properties with KC-16 including only the uppermost unit 17 .
Beryllium isotope analysis. Reactive Be ([ 10 Be] reactive and [ 9 Be] reactive ) was separated from marine sediments using the technique previously presented 29 . Approximately 0.1 g of sediment was dried and crushed before being leached with 0.04 M hydroxylamine hydrochloride in 25% acetic acid for 7 h at 80°C. An aliquot of the leached solution was measured for reactive 9 Be using a Thermo® ELEMENT XR high resolution inductively coupled plasma mass spectrometer (HR-ICP-MS) at the Atmosphere and Ocean Research Institute (AORI), the University of Tokyo (UTokyo), after spiking with 5 µl of indium (1 µg/g) solution 55 . The remaining solution was spiked with 1 ml of a 0.097 mg/ml 9 Be carrier before purification using two solvent extractions of acetylacetone in the presence of EDTA followed by precipitation of Be(OH) 2 with NH 4 (ref. 56,57 ). The resulting hydroxide was converted to BeO powder using a microwave ceramic crucible 58 before being mixed with niobium, inserted into a copper cathode, and measured by a National Electrostatic Corporation accelerator mass spectrometer (AMS) at the UTokyo Micro Analysis Laboratory, Tandem Accelerator (MALT) 59 .
Age-depth model. Radiocarbon analysis of two marine carbonate samples 33 and seven bulk samples 17 were previously obtained from KC-15. We provide a new agedepth model (Fig. S1) based on the modelling routine, Undatable, which uses the Bayesian 14 C calibration software, MatCal, to take into account analytical uncertainty associated with 14 C measurements and depth uncertainties of 2 cm (ref. 60 ). Carbon-14 ages were corrected for local effects 17,61 and a marine reservoir effect (ΔR) of 900 ± 100 years (ref. 62 ) prior to calibration using the Marine13 curve 63 .
Undatable was run for 10 6 iterations using a bootstrapping percentage of 20% and a Gaussian SAR uncertainty factor of 0.1 (ref. 60 ).

Data availability
All data generated in this study are included in the Supplementary information file.